After being convicted of a crime you are sentenced to 300 consecutive days in Cleveland. If you begin your sentence on Monday on what day of the week will your sentence end? Explain how you can relate this question to the ideas in this chapter.

The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

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The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28) ⇒ 1st answer

The figure consists of

Two hemispheres

A cylinder

The volume of the hemisphere = (2/3)πr³ , where r is its radius

The volume of the cylinder = πr²h, where r is its radius and h is its height

∵ The diameter of the hemisphere s and the cylinder is 20 units

∵ The radius =  1/2 diameter

∴ The radius = (1/2) × 20 = 10 units

∵ The volume of a hemisphere = (2/3) πr³

∵ r = 10

- Substitute r by 10 in the rule

∴ The volume of a hemisphere =  (2/3)π(10)³

∵ The volume of the cylinder = πr²h

∵ h = 28 and r = 10

Substitute h by 28 and r by 10 in the rule

∴ The volume of the cylinder = π(10)²(28)

∵ The volume of the figure = 2(volume of a hemisphere) +

  volume of the cylinder

∴ The volume of the figure = 2( 2/3 )π(10)³ + π(10)²(28)

∵ 2 × (2/3)  = 4/3

∴ The volume of the figure =  (4/3) π(10)³ + π(10)²(28)

The expression represents the volume in cubic units of the composite figure is (Four-third)π(10)³ + π(10)²(28)

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The complete question is:

Which expression represents the volume, in cubic units, of the composite figure?

(Four-thirds)π(103) + π(102)(28)

(Four-thirds)π(203) + π(202)(28)

2(Four-thirds)π(103) + π(102)(28)

2(Four-thirds)π(203) + π(202)(28)

The remaining angles of angle ABC and angle DEF are  right angles since they add up to 90 degrees.

Under the condition that angle ABC and angle DEF are both supplementary to angle XYZ, and angle XYZ is a right angle, then angle ABC and angle DEF are both right angles.

This is due to the supplementary angles add up to 180 degrees and since angle XYZ is a right angle (90 degrees), then angle ABC and angle DEF must be right angles since they add up to 90 degrees.

Supplementary angles are known as  two angles whose sum is 180 degrees . For instance, angle 130° and angle 50° are supplementary angles because the sum of 130° and 50° is equal to 180°. When supplementary angles are put together, they form a straight line and a straight angle.

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Answer:

The Answer is 11 and -1

Step-by-step explanation:

This factring unit can be tricky! Think about it this way. A prime number, such as 11 and 7 can only be factored with 1 and their own numbers. so 11 times -1 is 11 plus -1 is 10. Hope this helps and good luck!

a) To estimate the true average daily water consumption with a random sample of 100 water meters within a community, we can use the sample mean of 15.2. The sample variance of 1252 provides a bound on the error of estimation. The true average daily water consumption is estimated to be 15.2, with a bound on the error of estimation of 1252.

b) No, it is not reasonable to conclude that on average households in this community have a daily water consumption of 10 units. The sample mean of 15.2 indicates that households have an average daily water consumption of 15.2 units, not 10 units.

c) The assumption necessary in (a) in order to place the bound on the error of estimation is that the sample is a random sample. This assumption is necessary as it ensures that the sample mean is an unbiased estimate of the population mean and that the sample variance provides a bound on the error of estimation.

d) To estimate the total amount of water consumption in this community, we can use the sample mean from (a) and the total number of households in the community (9500). Thus, the total amount of water consumption in this community is estimated to be 143800 units, with a bound on the error of estimation of 1252.

e) We must sample 987 houses if we wish to estimate the average water consumption to within a bound of 5 units. This makes sense as the bound on the error of estimation in (a) was 1252, and 987 houses would decrease the bound on the error of estimation to 5 units.

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The expected number of adults who prefer coffee is 150.

We must determine the anticipated number of adults who prefer coffee in order to test for independence between age and drink preferences.

First, let's look at the totals of the rows and columns to figure out the expected values for each category. The formula is available to us:

Anticipated esteem = (Line absolute * Section complete)/Stupendous aggregate

The stupendous complete for this situation is 1000.

Number of adults expected to prefer coffee:

= (Adults total minus Coffee total) / Grand total = (600 minus 250) / 1000 = 150; consequently, 150 adults are anticipated to prefer coffee.

In this way, the right response is (a) 150.

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Answer:

sure, the answer is 50

Step-by-step explanation: Because this is a right triangle, you can use the pythagorean theorem, which is a^2 + b^2 =c^2 so you square 48 and add it to 14 squared and then take the square roo t to get the value of the hypotenuse, note that c will always represent the hypotenuse or longest side, and that pythagorean theorem can only be used on right triangles

Answer:

Rs.11,111.11 (2 d.p.)

Step-by-step explanation:

The original price of the mobile is 100% of the price.

Therefore, the price of the mobile after a discount of 10% is 90% of the original price.

Let x be the original price.

If the price of the mobile after the discount is Rs.10000 then:

⇒ 90% of x = Rs.10000

⇒ 0.9x = 10000

⇒ x = 10000 ÷ 0.9

⇒ x = 11111.11  (2 d.p.)

M.P. =Rs 11111.1111

Answer:

Solution Given:

Selling price (S.P.) = Rs 10,000.

Discount =10%

Marked Price (M.P.)=?

we have

M.P. = S.P. + discount% of M.P.

keeping M.P. on same side

M.P. - discount% of M.P=S.P.

substituting value

M.P. - 10% of M.P.= Rs 10,000

taking common M.P.

M.P.(1-10%)=Rs. 10,000

we know that %=1/100

M.P.(1-10/100)=Rs 10,000

(9/10)M.P.= Rs 10,000

M.P.= Rs 10,000*10/9

M.P.=Rs11111.1111

Answer:

[0,8]

Step-by-step explanation:

The lowest y value is 0

The highest y value is 8

We typically write range in interval notation

Interval notation goes from lowest value to highest value. Therfore the range is;

[0,8]

Answer:

It represents the product of two rational numbers and is equivalent to a rational number.

Step-by-step explanation:

\( \sqrt{25} = 5\)

because

\(5 \times 5 = 25\)

and

\( \sqrt{4} = 2\)

because

\(2 \times 2 = 4\)

The numbers are all rational because they can all be put into fraction form.

The complement set of S is {1, 3, 5, 8, 9, 10}.

To find the complement set of S, we need to identify all the elements in the universal set U that are not present in set S.

Given:

Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Set S = {2, 4, 6, 7}

The complement set of S, denoted as S', consists of all the elements in U that are not in S.

Complement set of S (S') = U - S

To find S', we subtract the elements of S from U:

S' = {1, 3, 5, 8, 9, 10}

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Answer:

9.54 cm

Step-by-step explanation:

In triangle ABD, AD is the hypotenuse (longest side)

We know that according to Pythagoras theorem,

a^2+b^2=c^2

In the figure, c (10cm) and a (5cm) is given. So,

(5)^2 + b^2 = 100

25+b^2 = 100

b^2 = 75

So b is √75 = 8.66

Therefore BD is 8.66 cm

Now even BDC is a triangle

In it, the hypotenuse is missing but we know the value of other sides

so, in Pythagorean theorem,

a=4 (CD)

b=8.66 (BD)

c=x

Therefore,

(4)^2 + (8.66)^2 = x^2

16+74.99= x^2

x^2 = 90.99

x= 9.54 cm

Hope this helps!

Answer:

80

Step-by-step explanation:

The researcher is measuring the reliability of a self-report test that measures anxiety in a group of participants. This is because if the test is not reliable, then we can not rely on the answers that participants give.

To measure reliability, the researcher is using split-half reliability by computing the correlation between the scores for the first 10 questions and the scores for the last 10 questions for each participant. This type of reliability measurement is commonly used with self-report tests and helps to determine how consistent the answers to the questions on the test are. If the two halves are highly correlated, then we can be more confident that the test is reliable.

An alternative measure of reliability is test-retest reliability, which assesses the consistency of a test over time. Test-retest reliability is calculated by administering the same test to the same group of participants on two different occasions and computing the correlation between the two sets of scores. If a test is reliable, then the scores obtained on the test should be relatively consistent over time.

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Answer:

Mya’s equation

Step-by-step explanation:

Given that:

Detergent left in bottle after a certain number of washes x

Dexter’s equation,

y= -1.6x+50

Mya’s equation,

y = 50(.75)x

y = Detergent left in bottle.

Given that amount of Detergent left is about 1/2 ounces = y

For Dexter’s equation,

y= -1.6x+50

0.5 = 1.6x + 50

0.5 - 50 = 1.6x

-45.5 = 1.6x

x = 28.4375

For Mya’s equation :

y = 50(0.75)x

0.5 = 37.5x

0.5 / 37.5 = x

0.0133333 = x

Hence, Mya’s equation

Answer:

116/8 - 87/8 = 29/8 = 3 5/8 gal

Step-by-step explanation:

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$500\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &5 \end{cases} \\\\\\ 500=P(0.04)(5)\implies \cfrac{500}{(0.04)(5)}=P\implies 2500=P\)

The amount of money, P, that will generate $500 at a 4% interest rate over 5 years is $2500.

By definition, simple interest is the interest amount for a particular principal amount of money at some rate of interest.

Mathematically, simple interest is

I = Prt,

where I represents the simple interest on an amount of money, P, for t years at r rate.

Now it is given that,

Simple interest, I = $500

Interest Rate, r =  4% = 0.04

Time, t = 5 years

Since, Simple interest, I = Prt

⇒ P = I/rt

⇒ P = 500/(0.04*5)

⇒ P = 500/0.20

⇒ P = $2500

which is the required Principle amount.

Thus, the amount of money, P, that will generate $500 at a 4% interest rate over 5 years is $2500.

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Using the z-distribution, it is found that the 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

We are given the standard deviation for the population, hence, the z-distribution is used. The parameters for the interval is:

Sample mean of  \(x = 12.7\)

Population standard deviation of  \(\sigma = 6.37\)

Sample size of .n = 50

The margin of error is:

\(M = z \frac{\sigma }{\sqrt{n} }\)

In which z is the critical value.

We have to find the critical value, which is z with a p-value of  \(\frac{1+\alpha }{2}\) , in which  \(\alpha\) is the confidence level.

In this problem, , thus, z with a p-value of , which means that it is z = 1.96.

Then:

\(M= 1.96\frac{6.37}{\sqrt{50} } = 1.77\)

The confidence interval is the sample mean plus/minutes the margin of error, hence:

x- M = 12.17 - 1.77 =10.4

x+M = 12.17 + 1.77 = 13.94

The 95% confidence interval for the mean lifetime of this type of drill, in holes drilled, is (10.4, 13.94).

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Answer:

By adding n = 10 to the calculation, we can determine the tenth component in the sequence denoted by the expression a(n) = 5n - 1:

a(10) = 5^10 - 1

= 976,5624

The sequence's tenth term is 976,5624 as a result.

The factor of negative 1 will be -1

Now, According to the question:

What is factor?

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product.

There are two methods of finding factors: multiplication and division. In addition, rules of divisibility may also be used.

Hence, Every negative number can be thought of as having some positive factors and exactly one negative factor, -1. When a positive number and a negative number are multiplied, the product has that one -1, so it's negative.

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The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons, is approximately 0.54.

(a) The probability that the person is traveling on business is 0.7(0.5) + 0.3(0.7) = 0.56.

(b) The probability that the person is traveling for business on a privately owned plane is 0.3(0.7) = 0.21.

(c) The probability that the person arrived on a privately owned plane, given that the person is traveling for business reasons, is given by Bayes' theorem as:

P(private plane | business) = P(business | private plane) * P(private plane) / P(business)

= (0.7 * 0.3) / (0.7 * 0.5 + 0.3 * 0.7) = 0.3 / 0.56 ≈ 0.54.

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The fifth term of the arithmetic sequence is -1190.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. To find the fifth term, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1) * d

where aₙ represents the nth term, a₁ is the first term, n is the position of the term, and d is the common difference.

Given that the 100th term is -1240 and the common difference is -25, we can substitute these values into the formula.

Since the fifth term corresponds to n = 5, we can calculate:

a₅ = -1240 + (5 - 1) * (-25)

= -1240 + 4 * (-25)

= -1240 - 100

= -1340

Therefore, the fifth term of the arithmetic sequence is -1190.

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If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.

On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.

Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.

Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.

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Answer:

8

Step-by-step explanation:

Let's say that the amount of lollipops Lydia buys is represented by x and the number of candy bars is represented by y. For each x, Lydia spends 0.50, and for each y, Lydia spends 1.50. This means that the total amount she spends can be represented by the equation 0.50*x+1.50*y. Our equation is then 0.50*x+1.50*y=15

Using our equation, we can plug 6 in for x, resulting in 0.50*6+1.50*y=15, so \(0.50x+1.50y=15\\0.5(6)+1.50y=15\\3+1.50y=15\\1.50y=12\\y=8\)

In this set of equations, we plugged 6 in, multiplied it out, then subtracted 3 from both sides, and finally divided both sides by 1.50 to get 8 as our answer.

Answer:

Mass is a constant, weight would be 8.4kg as it's double the force pulling down on the object.

Step-by-step explanation:

From the given data, we can see that only one condition is violated, which is the sample size being less than 10% of the population size. The other conditions, such as the population distribution being approximately normal, np > 10, and n(1-p) > 10, are all satisfied. Therefore, the statement "more than one condition is violated" is incorrect.

Only one condition is violated in the given data, which is the sample size being less than 10% of the population size. The other conditions are all satisfied and do not violate any of the conditions for a representative sample.

It is important to note that in order for a sample to be representative of the population, the sample size should be at least 10% of the population size. If the sample size is less than 10% of the population size, the sample may not accurately represent the population and the results may be biased.

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The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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